All planes are of the form X=a+t.b+s.c where t,s€|R.Then the panle passes through a and parallel to both b and c.Hence X represents a plane if b and c are parallel.For option (b) we see that -1/2=2/(-4)=1/(-2).Therefore [-1 2 1]^T and [2 -4 -2]^T are parallel.Therefore option (b) represents a plane.
Which of the following equations define a plane? 2 ド!..lil..lil,r..e R ''X-H-N+3하a,JER Which of the foll...
1. Which of the following equations define a plane?
1. Which of the following equations define a plane?
1. Which of the following equations define a plane? 2 2 3 '7,S IR r21 T37
1. Which of the following equations define a plane? 2 2 3 '7,S IR r21 T37
2. Lil 0.5 H し22 = 2 H L121 sin , H e, 2" (a) Tai, 12,6%) N-m (b) If 1,-5 cos 20t A, 1,-1 A, and θ,-20t, T.(t) N-m Simplify to extent possible. (Sum of trig functions of time OK. Products of trig functions not OK). Show work below.
Define a relation R from R to R as follows: For all (x, y) E R x R, (x, y) E R if, and only if, x= y2 + 1. (a) Is (2, 5) E R? Is (5, 2) e R? Is (-3) R 10? Is 10 R (-3)? (b) Draw the graph of R in the Cartesian plane. (C) Is R a function from R to R? Explain.
A plane wave expressed in SI units E-3, n(r) is normally impinging on a polarizer of which the transmission axis is along the x-direction. How much irradiance can be received after the polarizer? (?: 4? x 10-7 H/m) 4.
Define a relation R on N x N by R = {(x,y) | x ε N, y ε N and x+y is even} Prove or disprove: R is an equivalence relation.
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x denotes the dot product of the vectors a and x. (i) Show that H is a subgroup of R (ii) For λ E R, show that : a·x= is a coset of H in R3. (ii) Is H cyclic? Prove or disprove.
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x...
*14. Let A be an n x n matrix. Define f:R" R by f(x) = Ax.x = x'AX. (a) Show that f is differentiable and Df (a)h = Aah + Ah a. (b) Deduce that when A is symmetric, Df(a)h = 2Aa . h. 15. Let a € R", 8 >0, and suppose f: B(a, 8) - R is differentiable at a. Suppose f(a) f(x)
Let A be n × n with AT-A. (The matrix A is syrnmetric.) Let B be 1 × n and let c E R. Define f : Rn → R by f(x) = 2.7, A . x + B . x + c. Show that The function f is a quadratic function
Let A be n × n with AT-A. (The matrix A is syrnmetric.) Let B be 1 × n and let c E R. Define f : Rn...
a through e is considered one question.
7.Let A be ann x n real symmetric invertible matrix, let B Rt and C E R. Define f:R R by 2 a. Give f (a) c. Give f"(x) d. Prove that if A is positive definite and u is the critical point of f, then f(u) < f(x) for all x E Rn where x Prove that if A is negative definite and u is the critical point of f, then f(u)...